I have a survey with categorical (nominal) questions. I want to compare subgroups to see if any are noticeably different from each other. Suppose they are ranking their preferred three from ten flavours of ice creams. Suppose there are 75% male and 25% female respondents. 20% of males like chocolate while 30% of females do. The population average is therefore 22%. I can do a Z test. Do I compare the preferences of males to the population average or to the population excluding the males, ie the females ? Depending on the sample size 20% may not be significantly different from 22% but it may be different from 30% ; or the other way around, 30% may be less significantly differently from 22% than from 20%. The high proportion of males dominates the average, so the male association will not appear significantly different from the population. The question is : for chocolate flavour, are females more strongly associated with chocolate than male and what confidence can we have in saying that? The harder question is, when I have more than two subgroups eg comparing people in six different areas how can I say which pairs are significantly different from each other; or from the rest of the groups excluding the group in question?


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